Optical bandpass filters that rely on birefringence are known in a number of different configurations. Birefringence is a characteristic of certain crystals wherein there is a difference in optical index for orthogonal light components that are aligned to the respective fast and slow axes of the crystal. If a plane polarized input light signal is aligned at 45° to the fast and slow axes a birefringent crystal, for example, the crystal induces a differential phase retardation between a component that is parallel to the slow axis versus the component that is parallel to the fast axis.
The differential retardation produces a change in polarization state of the light that propagates through the crystal. Polarization state is partly a matter of the phase relationship between orthogonal light components. Assuming that the incident light components were in phase and of equal power, etc., differential retardation induces a rotation in the polarization alignment of the light by a rotation angle related to the crystal thickness and birefringence.
The rotation angle is a function of wavelength, because a given difference in propagation time or distance along an optical propagation path (caused by the difference in optical index) amounts to a greater phase angle if the wavelength is shorter, and a smaller phase angle if the wavelength is longer.
In this way, birefringence along an optical path induces a polarization realignment that is a function of wavelength. The effect can provide a wavelength filter. If one passes light through a plane polarizing filter, a birefringent crystal and a second polarizing filter, the combination will discriminate for those wavelengths at which the polarization realignment through the crystal corresponds to the rotational difference in the alignment of the polarizers. This correspondence occurs at multiple wavelengths at which the differential retardation produces rotation in integer multiples of π radians (180°).
There are certain known birefringent filter configurations that use birefringence and polarizing filters to discriminate by wavelength. These filters typically have multiple birefringent retarders and can also have multiple polarizing filters. Examples are the so-called Lyot, Lyot-Ohman, Solc and Evans birefringence filters. One difference between these filters is the manner in which the thicknesses of the multiple retarders are made equal or are varied. Another difference is the manner in which the rotational alignment of the retarders differs. The idea in each case, however, is to provide a polarization state change through the respective retarders that results in alignment of the desired wavelength to the output polarizing filter, and to exclude other wavelengths.
Multiple stages of birefringence and/or polarization filtering can be disposed serially to obtain better wavelength discrimination, but there are complications. For example, if the stages have bandpasses that are not well aligned, particularly if subject to tuning, then desired light energy may be blocked rather than passed. Each successive filter stage is likely to cause some transmission loss. There is a tradeoff between design choices that might make the wavelength bandpass more discriminating versus choices to improve the ratio of passed light energy. Each polarizer typically has an inherent transmission loss, even with respect to light energy that is plane polarized and aligned to the polarizer. The particular loss varies with the wavelength and the polarizer used, but might be, for example 12%. If a large number of stages are needed to provide a high degree of discrimination or a very narrow bandpass, the level of light energy passing the filter may be low. A low transmission ratio may require that light energy be collected for a relatively long time to obtain an image or a measurement.
Discrimination for a particular wavelength by altering polarization state produces a wavelength-periodic result. If the differential delay is 2π radians or an integer multiple thereof, for example, the effect is the same as no delay. Considering plane polarizers, if a polarization state is changed by a differential phase delay of an integer multiple of a radians (180°), the rotated polarization state is again parallel to the polarizer. For these reasons, filters having one or more retarders and plane polarizing filters pass light at multiple wavelengths.
Birefringence interference filters with plural stages were developed for observing solar spectra. The retarder birefringence and thickness parameters were chosen to pass certain very specific, narrow and well defined spectral lines in the emission spectrum of solar radiation. Sub-angstrom spectral resolution is said to be obtained using the filter developed by B. Lyot (See, Comptes rendus 197, 1593 (1933)). A basic Lyot filter comprises a number of filer stages placed successively along a light path. (See, Yariv, A. and Yeh, P. (1984) Optical Waves in Crystals, Chapter 5, John Wiley and Sons, New York). Each stage has a birefringent crystal element (a retarder) between parallel polarizers. The exit polarizer of one element can function as the input polarizer of the next element.
Lyot birefringent crystals have optical axes parallel to the interface and rotated by 45 degrees to the direction of the input polarization, thus dividing the light from the input polarizer into two components divided equally between the fast and slow axes of the birefringence crystal. In propagating through the crystal, the component on the slow axis becomes retarded relative to the component on the fast axis. The polarization orientation of the light is altered as well. At the output, the exit polarizer at 45 degrees to the preceding crystal retains equal proportions the retarded and the un-retarded components, but passes only that wavelength or wavelengths for which the angular polarization change through the crystal is the same as the relative alignment of the input and output polarizers (or that differs by an integer multiple of 180 degrees).
A Lyot filter has a repetitive layout of crystals between polarizers, each the crystals and their polarizers being relatively aligned at 45 degrees. The phase differences in Lyot are introduced in part because the thickness of each stacked birefringent crystal elements is different. The thickness and the birefringence each contribute to the retardation introduced. In the Lyot configuration, the retardation produced by the crystal at each stage is precisely twice the retardation from the crystal at the preceding stage. The bandpass wavelength is related to the thickness and birefringence of the crystals.
The successively varying stage thicknesses are selected (e.g., 1d, 2d, 4d, 8d, etc. for Lyot) with regard to the relative rotational alignment of the successive stages, so as to provide an arithmetic, geometric or other mathematical progression. The operation of the stages can be modeled mathematically and tested empirically. Multiple stage crystal devices have been demonstrated with 0.1 angstrom resolution (Title, A. M. and Rosenberg, W. J. Opt. Eng. 20, 815 (1981)). In order to achieve such resolution, dimensional precision is necessary, which makes the filters expensive. Often, resolution is improved simply by adding to the number of successive cells, sometimes using a large number of successive cells. This has the disadvantage of reducing the proportion of light that is transmitted versus the proportion that is rejected. Such filters are suited for astronomical applications wherein the filters are tuned to specific lines of the solar spectrum, where the source, like the Sun, is very bright.
Another configuration of stacked crystal filter was developed by L. Solc. Like Lyot, the Solc filter uses multiple birefringent crystals in a stack, but unlike Lyot, the Solc filter uses equal retarder thicknesses and does not require a polarizer between each retarder. The Solc configuration requires that the orientation of the successive retarders have a particular relationship, specifically to distribute evenly among successive retarders a rotational progression of the desired wavelength by a specific rotational angle. A single output polarizer (sometimes called the analyzer) is oriented at the corresponding rotational angle and receives and passes the desired wavelength. Solc filters are described, for example, in Solc., J. Opt. Soc. Am. 55, 621, (1965).
The relative rotational angles between each birefringent crystal and the next preceding or succeeding crystal in a Solc configuration thus represent fractions of the rotation angle between the entrance and analyzer polarizers that precede and follow the stack of retarders. The Solc “fan” filter configuration has N identical crystals with rotation angles of θ, 3θ, 5θ . . . (2N−1)θ, located between parallel polarizers where θ=π/4N, and N is the number of crystals in the stack. Thus, Solc fan angles are progressively more rotated in a same direction. The Solc “folded” configuration has N identical crystals oriented at ±θ with respect to the incoming polarization where θ is the angle which the optic axis the crystal makes with the transmission axis of the entrance polarizer. The folded design has alternating orientations and uses crossed polarizers, but otherwise operates in the same way as a fan configuration to orient the polarization state of the selected bandwidth so as to pass the exit polarizer. Among other varieties of recognized Solc configurations are the Solc Gaussian and Solc sine configurations.
For example, a Solc “fan” arrangement might have four retardation elements and parallel polarizers. In such a Solc “fan” arrangement of four crystals (N=4), the first crystal is rotated 11.25 degrees relative to an input polarizer. The successive crystals are rotated by 22.5 degrees relative to the next preceding crystal. The output or analyzer polarizer is parallel to the entrance polarizer. A four retarder Solc “folded” arrangement by comparison has four stacked crystals placed alternately at clockwise and counterclockwise rotation angles relative to the polarizer, such as +11.25 degrees, −0.25, +11.25, and so on, and the analyzer polarizer is perpendicular to the entrance polarizer. Other variants are possible with different values for N, θ and the orientation of the polarizers.
In Harris et al., J. Opt. Soc. Am. 54, 1267, (1964) it is posited that any filter transmission function might be generated, in principle, using a stack of properly configured retardation plates. Researchers have used the network synthesis technique, along with standard signal processing methods, to generate filter designs based on this premise. These designs have sought high resolution over a limited spectral range, as opposed to a broad spectral range. The filters typically have fixed retardation elements. When tuning is to be considered, the retardances can be varied in unison.
Known multiple-retarder configurations of the type described each have advantages and disadvantages, in a Solc configuration, for example, the crystals are all of the same thickness. Equal retarder stages may be less expensive and more easily manufactured than coordinated varying thicknesses. A larger number of stages will fit in a longitudinally shorter stack than in a Lyot configuration with progressively varying thicknesses. A Solc configuration uses relatively fewer polarizers than some of the alternatives.
There exists a need for a highly accurate spectral imaging filter configured to operate over the range from visible to infrared (VIS-NIR), approximately 400-1100 nm, including the upper and lower limits of the range. Such a spectral filter holds potential for application in spectroscopic and hyperspectral imaging configurations. It would also be advantageous for such a filter to provide for fast switching speeds and a high out-of-band ratio.